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Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?1. 30 / 72. 20 / 73. 50 / 74. 15 / 7 |
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Answer» Correct Answer - Option 1 : 30 / 7 Given: Time to fill the tank by two pipes = 15 hours and 4 hours Time to empty the tank by third pipe = 12 hours Concept used: If Pipe A take ‘x’ hours and Pipe B takes ‘y’ hours to fill a tank then assume total capacity of the tank equal to LCM of ‘x’ and ‘y’ or a multiple of them. Formula used: Efficiency = Total work/total time Calculations: Let total capacity of tank be LCM of 15, 4 and 12 i.e. 60 units. Efficiency of first pipe = 60/15 ⇒ 4 units/hour Efficiency of second pipe = 60/4 ⇒ 15 units/hour Efficiency of third pipe = 60/12 ⇒ 5 units/hour Combined efficiency of three pipes = 4 + 15 - 5 ⇒ 14 units/hour Time to empty the tank by all the pipes together = 60/14 ⇒ 30/7 hours ∴ It takes 30/7 hours to fill the empty tank if all the three pipes are opened simultaneously. |
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